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Let S be the set {1, 2, 3, \dots, 10, 11, 12}.  How many subsets of the set S have no two consecutive primes as members?

 Mar 7, 2025
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Let S be the set {1, 2, 3, \dots, 10, 11, 12}.     

How many subsets of the set S have no two consecutive primes as members?     

 

I don't know how many subsets exist in set S, but the only consecutive primes in the set are 2 and 3.     

So figure up all the subsets, then eliminate the ones that contain 2, 3.  BTW, 1 is not a prime number.   

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 Jul 2, 2025

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